The Kerr/CFT correspondence and its extensions: a comprehensive review

TL;DR

This comprehensive review derives key results of the Kerr/CFT correspondence and its extensions using gravity and quantum field theory, highlighting the role of conformal symmetries in black hole entropy and dynamics.

Contribution

It provides a first-principles derivation of Kerr/CFT results, including asymptotic symmetries and entropy matching, and explores extensions to non-extremal black holes and supergravity theories.

Findings

Matching black hole entropy with Cardy's formula

Identification of asymptotic Virasoro symmetry in near-horizon regions

Reproduction of near-superradiant probe dynamics via 2D CFT

Abstract

We present a first-principles derivation of the main results of the Kerr/CFT correspondence and its extensions using only tools from gravity and quantum field theory. Firstly, we review properties of extremal black holes with in particular the construction of an asymptotic Virasoro symmetry in the near-horizon limit. The entropy of extremal spinning or charged black holes is shown to match with a chiral half of Cardy's formula. Secondly, we show how a thermal 2-dimensional conformal field theory (CFT) is relevant to reproduce the dynamics of near-superradiant probes around near-extremal black holes in the semi-classical limit. Thirdly, we review the hidden conformal symmetries of asymptotically-flat black holes away from extremality and present how the non-extremal entropy can be matched with Cardy's formula. We follow an effective field theory approach and consider the Kerr-Newman black hole and its generalizations in various supergravity theories. The interpretation of these results by deformed dual conformal field theories is discussed and contrasted with properties of standard 2-dimensional CFTs. We conclude with a list of open problems.